Melt butter with olive oil in a large pot over medium heat. Add diced onions and cook until they’re soft and translucent, about 5 minutes. Add garlic and cook for another minute until fragrant.

Add the sliced mushrooms and 2 teaspoons of thyme. Stir and cook until the mushrooms release their moisture and turn golden brown, about 8–10 minutes.

Sprinkle in the flour and stir well for 1 minute to cook it through. Add salt, pepper, and dried tarragon. This gives the soup its thick, velvety texture.

Slowly pour in the chicken or vegetable broth while stirring to avoid lumps. Bring the soup to a simmer and let it cook for about 10 minutes.

For a smooth soup, use an immersion blender or transfer half the soup to a blender, then return it to the pot. If you prefer chunky, skip this step — both versions taste amazing.

Reduce heat to low, stir in the milk and heavy cream, and let it warm through. Don’t boil at this point — you just want it gently heated.

Taste and adjust seasoning. Garnish with chopped fresh thyme and parsley before serving.